Weak compactness of almost limited operators

The paper is devoted to the relationship between almost limited operators and weakly compacts operators. We show that if $F$ is a $\sigma$-Dedekind complete Banach lattice then, every almost limited operator $T:E\rightarrow F$ is weakly compact if and only if $E$ is reflexive or the norm of $F$ is order continuous. Also, we show that if $E$ is a $\sigma$-Dedekind complete Banach lattice then the square of every positive almost limited operator $T:E\rightarrow E$ is weakly compact if and only if the norm of $E$ is order continuous.Comment: 5 page

Banach lattices with the positive Dunford-Pettis relatively compact property

The paper is devoted to such Banach lattices E that every Dunford-Pettis and weakly null sequence (x_n) ⊂ E with disjoint terms is norm null (the positive Dunford-Pettis relatively compact property). It is established that a Banach lattice E has the positive Dunford-Pettis relatively compact property if and only if its almost Dunford-Pettis subsets are L-weakly compact. Consequently, we derive the following result: Banach lattices with the property that their almost Dunford-Pettis subsets are relatively compact, are precisely the discrete KB-spaces.peerReviewe

HCCI engine modeling and experimental investigations - Part 2: The composition of a NO-PRF interaction mechanism and the influence of NO in EGR on auto-ignition

This article presents an investigation of the effect of NO in EGR on HCCI auto-ignition, by means of experiments and a NO-PRF interaction mechanism. The influence is investigated both numerically and experimentally. The numerical part is effected by a composition of a NO submechanism and the subsequent addition of this sub mechanism to a reduced validated n-heptane/iso-octane PRF mechanism, the latter of which is presented in a previous article, named article 1 (Machrafi et al., submitted 2006). The experimental part is effected on a CFR engine, operating at HCCI conditions, with an inlet temperature of 70 degrees C and a compression ratio of 10.2. Hereby n-heptane and PRF40 are used as the fuels, using different equivalence ratios in order to extend the interpretation domain. The NO adding concentration is experimentally varied between 0 and 160 ppm. The results showed that adding NO at low concentrations advances the ignition delays, the promoting reactions being more reactive than the inhibitory ones. The promoting effect seems to be at its maximum at an addition of 45 ppm concerning the fuel PRF40. At higher adding concentrations of NO the promoting effect becomes less and the inhibitory reactions become more reactive. The effect of NO on the auto-ignition of n-heptane seemed, however, to be unsignificant. The effect of NO was qualitatively well represented by the mechanism, while quantitatively the mechanism predicted a lower effect of NO at an addition of 45 ppm

Some characterizations of KB-operators on Banach lattices and ordered Banach spaces

We determine that two recent classes of KB-operators and weak KB-operators and the well-known class of b-weakly compact operators, from a Banach lattice into a Banach space, are the same. We extend our study to the ordered Banach space setting by showing that a weak chain-preserving operator between two ordered Banach spaces is a KB-operator if and only if it is a weak KB-operator

Time-dependent Marangoni-Bénard instability of an evaporating binary-liquid layer including gas transients

info:eu-repo/semantics/publishe

Evaporation Rates and Bénard-Marangoni Supercriticality Levels for Liquid Layers Under an Inert Gas Flow

In this work, we propose an approximate model of evaporation-induced Bénard-Marangoni instabilities in a volatile liquid layer with a free surface along which an inert gas flow is externally imposed. This setting corresponds to the configuration foreseen for the ESA-"EVAPORATION PATTERNS" space experiment, which involves HFE-7100 and nitrogen as working fluids. The approximate model consists in replacing the actual flowing gas layer by an "equivalent" gas at rest, with a thickness that is determined in order to yield comparable global evaporation rates. This allows studying the actual system in terms of an equivalent Pearson's problem (with a suitably defined wavenumber-dependent Biot number at the free surface), allowing to estimate how far above critical the system is for given control parameters. Among these, a parametric analysis is carried out as a function of the liquid-layer thickness, the flow rate of the gas, its relative humidity at the inlet, and the ambient pressure and temperature. © 2013 Springer Science+Business Media Dordrecht.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Bénard instabilities in a binary-liquid layer evaporating into an inert gas: stability of quasi-stationary and time-dependent reference profiles

This study treats an evaporating horizontal binary-liquid layer in contact with the air with an imposed transfer distance. The liquid is an aqueous solution of ethanol (10 % wt). Due to evaporation, the ethanol mass fraction can change and a cooling occurs at the liquid-gas interface. This can trigger solutal and thermal Rayleigh-B´enard-Marangoni instabilities in the system, the modes of which corresponding to an undeformable interface form the subject of the present work. The decrease of the liquid-layer thickness is assumed to be slow on the diffusive time scales (quasi-stationarity). First we analyse the stability of quasistationary reference profiles for a model case within which the mass fraction of ethanol is assumed to be fixed at the bottom of the liquid. Then this consideration is generalized by letting the diffusive reference profile for the mass fraction in the liquid be transient (starting from a uniform state), while following the frozen-time approach for perturbations. The critical liquid thickness below which the system is stable at all times quite expectedly corresponds to the one obtained for the quasi-stationary profile. As a next step, a more realistic, zero-flux condition is used at the bottom in lieu of the fixed-concentration one. The critical thickness is found not to change much between these two cases. At larger thicknesses, the critical time at which the instability first appears proves, as can be expected, to be independent of the type of the concentration condition at the bottom. It is shown that solvent (water) evaporation plays a stabilizing role as compared to the case of a non-volatile solvent. At last, an effective approximate Pearson-like model is invoked making use in particular of the fact that the solutal Marangoni is by far the strongest as an instability mechanism here